I decided to take a look at our atDNA matches that I've confirmed a shared ancestors with to see the patterns of inheritance for each generation.
Most of these charts compare my mother and myself to various confirmed surname matches.
We'll start by comparing myself with my first cousin:
First Cousin Match
I don't have any second cousin matches
Third Cousin Matches
Fourth Cousin matches
Fifth Cousin Matches
Seventh Cousin matches
Tenth Cousin Match